Tossing three dices, how many combination of the sum (from 3 to 18)? I just found a general expression to find out such combination, which is (x + x^2 + x^3 + x^4 + x^5 + x^6)^3 the total combination of given sum for three dices is the coefficient of the corresponding term, for example, for the sum 10, the total combination is 27, which is the coefficient of the 10th term (x^10). I wonder how people find such expression? Why the combination is just the coefficient? Someone told me it is just a coincident, which is hard to convince me.